Problem of evil
Suppose we have the following four premises:
We get the following contradiction. If God is omnibenevolent, then he does not want evil to exist. If God is omniscient, then he must know about all evil in the world. If God is omnipotent, then he must be capable of doing something about it. Therefore, evil should not exist. Dropping any one of those four premises would resolve the contradiction, but dropping #4 would require us to fundamentally redefine evil in some way, and dropping the other three would undermine the Christian concept of God.
"Is He willing to prevent evil, but not able? Then He is impotent. Is He able, but not willing? Then He is malevolent. Is He both able and willing? Whence then is evil?"
- — Dialogues Concerning Natural Religion
(1) If God exists he is omniscient, omnipotent, and wholly good.
[Hypothesis that the theists' God exists]
(2) Evil occurs.
[Statement of the undisputed fact of evil]
(3) If someone did not prevent the occurrence of evil despite having full knowledge in advance that it would occur if he were not to prevent it and despite also having unlimited power to prevent it, then that person is morally culpable for its occurrence.
[Generalized principle of command responsibility]
(4) By virtue of his omniscience, God knew in advance that evil would occur unless he was to prevent it.
[From 1 by definition of omniscience]
(5) By virtue of his omnipotence, God had the ability to prevent the occurrence of evil.
[From 1 by definition of omnipotence in terms of absence of nonlogical limits to God's ability]
(6) God did not prevent the occurrence of evil.
[From 2 by double negation]
(7) God had the ability to prevent evil from occurring and knew it would occur if he did not prevent it.
[From 4 and 5 by conjunction]
(8) God is morally culpable for the occurrence of evil.
[From 3 and 7 by modus ponens]
(9) God is not wholly good.
[From 8 by definition of "wholly good"]
(10) God does not exist.
[From 1 and 9 by modus tollens]
A theodicy is a proposed solution to the problem of evil. Coined by Gottfried Leibniz in 1710, in a work called "Theodicy Essay on the Benevolence of God, the Free will of man, and the Origin of Evil".
A theodicy can generally be divided into four categories, each typically rejecting one of the four premises used to make the argument. The argument is, after all, not an argument for the non-existence of God but an argument for the non-existence of God with the characteristics of omniscience, omnipotence, and omnibenevolence in the presence of evil. Some arguments aren't solutions to the problem but justifications.
When compared to a easily prevented, extremely "evil" act, such as the rape and murder of a child, or a gross atrocity like the holocaust, slavery or other genocides, most theodicies crumble, quickly exposing them as sophistry with worse implications than the original problem.
God is not omnipotent
It is often claimed that evil exists because God gave humans free will. According to the Bible, God's gift of free will led to the fall of Adam and Eve through their original sin. Free will is assumed to be a greater good than the evil that it causes or is needed by God to serve some purpose. For example, free will is required for people to love God in a free and open fashion. So if a young girl is raped and murdered, this is because God needed the rapist's free will so that his actions could result in greater good or so that the rapist could freely love God.
As Mackie asked: "Why could [God] not have made men such that they always freely choose the good?" Even if man is believed to have free will, God could have created humans such that they would always freely choose the good. This he did not do and is therefore ultimately responsible and blameworthy for any evil act which humans perform.
Of course, God is supposedly free-willing and omnibenevolent, so the two properties do not contradict in God's case. Why then should humans be any different if it is logically possible in God's case? It is important to realize that free will is different than will power. If God intentionally made humans extremely fallible then the consequences are ultimately God's responsibility.
Gale's response: He (Gale) claims that "God's way of causing created persons to act /…/ is freedom canceling." That is to say, humans are not free agents and hence not ultimately blameworthy for their acts of evil. He lists certain freedom-canceling sufficient conditions:
The case of the sinister cyberneticist: "C1. If M1's actions and choices result from psychological conditions that are intentionally determined by another man M2, then these actions and choices are not free." The case of the evil puppeteer: "C2. M2 has a freedom-canceling control over M1 if M2 causes most of M1's behavior."
"Is God's relation to created persons in the FWD such that it satisfies C1 and/or C2? If it satisfies either, no less both, the FWD is in trouble, as would be the soul-building defense as well. I submit that it satisfies both, and thus it is time for the nervous smile to replace the smirk."
"It is clear that it satisfies C1, since according to the FWD, God intentionally causes a created free person to have all of her freedom-neutral properties, which include her psychological makeup. The Free Will Defender will make the Libertarian claim that these inner traits only 'incline,' but do not causally determine, the person to perform various actions or act in a certain regular manner, but this does not make the God-man case significantly disanalogous to the type-1 man-man cases; for even if we imagine that our intentional psychological-trait inducers could render it only probably according to various statistical laws that their victims would behave in certain characteristic ways, they still would exercise a global freedom-canceling control in which the person is rendered nonfree due to her not having a mind of her own."
"The God-man relation in the FWD also satisfies C2; for, when God instantiates diminished possible persons or sets of freedom-neutral properties, he does have middle knowledge of what choices and actions will result, and thereby sufficiently causes them. And he does so quite independently of whether or not he is blameless for the untoward ones among them."
This argument fails in that free will is given a definition which relies on the ability to perform actions. The implication is that humans must be free to commit actions which would qualify as "evil" as well as "good" in the argument, in order to have free will. In this case, all humans born without this capability, possess no free will. Also, those who have an advantage, of strength, size, or skill, are presumably, more free in their will, in comparison to their potentially smaller, weaker, or less skilled, victims. Therefore, this objection to the problem of evil can only apply where this standard for free will is actually applied. Paradoxically, this puts God in the position of denying free will to someone regardless of God's position on an action, whether God intervenes, or not.
This argument also fails to explain why God allows natural disasters, such as hurricanes, tsunamis, and earthquakes. These events kill large numbers of people in specific geographical locations, which indicates that the concept of "evil" is not necessarily tied to what people do. Furthermore, it fails to account for evil done to people against their will. The argument of free will is used to justify why a infant can be killed, however the infant invoked no measure of free will to allow for this evil to result. So in order to give the gift of free will to this infant, the child is murdered without having any choice in the matter.
Even if we define natural disasters as not being evil, there remains the fact that they occur, and that God does not prevent them or the deaths and suffering they cause. If we replace "evil" with "suffering" in the discussion above, the problem remains: either God is unaware of people's suffering, and is therefore not omniscient; or he is unable to do anything, and is therefore not omnipotent; or he is unwilling to intervene, and is therefore not omnibenevolent.
There is also the question of heaven. Heaven, being a perfectly wonderful place, does not contain evil. Does this mean that inhabitants of heaven no longer retain their free will? Or does their will suddenly become perfectly good?
See also: The Free Will Defense Refuted and God's Existence Disproved 
Best of all possible worldsApologists such as Alvin Plantinga have made the claim that although there may be some evil in the world, this is in fact the best of all possible worlds.
This theodicy suggests that no improvement may be made to the world. Preventing children from dying in a tsunami or the holocaust from happening would be impossible for God. Plantinga argues that God's power is limited in that he cannot sin and cannot violate free will. However, there are plenty of improvements one could make to this world without violating free will or requiring God to sin.
Although it is not a direct problem with the claim itself, it is important to note that many theists who propose this claim also believe in Heaven, which is believed to be an even better world than this one. If this is the best world able to be created then Heaven cannot be created.
See also: The Free Will Defense Refuted and God's Existence Disproved 
Apologists often claim that what appears to be harmful to humans may, in fact, be for humanity's good. How can we learn, the argument goes, without making our own mistakes?
The "tough love" argument only works if God is limited in power. If God is omnipotent there is nothing he can not teach us gently that he can teach us harshly. If he is benevolent than he would never choose to teach us a harsh lesson when it could be taught, with exactly the same impact, gently.
Another problem with this argument is that although according to this argument, God wants us to grow as people by learning from our mistakes, according to most religious doctrine he also wants worship. Worship involves complete obedience and submission, whereas learning from mistakes requires using one's intelligence. It is contradictory to claim that God wants us to be both completely obedient and make decisions for ourselves, since complete obedience means blindly obeying authority, for example the story of Abraham and Issac (Genesis 22:1-19 ). Abraham was called "righteous" because he blindly obeyed God's command to murder his son. The fact that God stopped Abraham before the knife fell means nothing- even if he had allowed the murder, Abraham would still be called righteous for obeying God's command.
Really powerful, not all-powerful
God is not all-powerful in the sense that he can create a rock so heavy that even he cannot lift it. So, God is omnibenevolent, omniscient, and really really powerful.
If a child is raped and killed, is this because God is not powerful enough to prevent it? I could prevent that and would strive to with the smallest degree of foreknowledge. So if this argument is to succeed it must conclude that I am more powerful than God. And more benevolent.
God does not exist
God is unable to prevent evil because God does not exist. Argument does not apply to non-existing gods.
God is not omnibenevolent
One way to redefine the term 'benevolence' is to cite limited human perspective in space and time. A parent might spank a child for running into traffic, or take a child to the doctor for painful, life saving, injections. It is only in the limited, child's-eye-view that these things are malevolent.
As with the "tough love" argument, this view of God implicitly denies his omnipotence or, at least, his omniscience. What kind of parent purposely takes his child for a surgery which he knows the child does not need or want?
Another way to redefine 'benevolence' is to argue that God may be benevolent to specific humans or to non-humans. Our entire history may exist for the positive influence it may have on aliens we have not met. We may be actors in a puppet show that makes these beings happy. After all, it is perfectly possible for benevolent humans to play comically violent video games with their delighted children.
But this argument is sophistry. To win the argument the apologist defines a God that neither we nor he would have much reason to worship. For example, if the creatures in a violent "Run and Gun" video game were to gain self awareness, would we expect them to view us as benevolent beings worthy of their love and trust as we blast them into electronic oblivion?
And, if God is not benevolent toward humans, then what differentiates him from a human sociopath or from the Devil?
The problem of evil must be taken up in the context of humanity. No other context would make a God useful to humans in any realistic way. A God that is benevolent to others at lethal expense to humans is, by definition, malevolent, or at least indifferent, toward humans. It is an unusual apologist indeed who believes in this type of God.
God is benevolent to the point of impotence
Some claim that since God is omnibenevolent, he loves all his creatures, even Satan, who is considered by many to be the embodiment of evil. Therefore it would violate his omnibenevolence to simply destroy Satan or any other evil creation. This of course implies that God is not omnipotent. It is also contradicted by the Bible, which states that God hates evil.
Evil is a consequence of disobeying God
Evil exists not because it was created by God but because it results from our disobeying God's divine laws.
This explanation argues that God has created a earthly consequence for disobeying divine laws. There are two problems with this argument: 1. Innocents being victims of evil. 2. Immoral people escaping earthly consequence. If this argument was indeed true, infants, children, and otherwise good people would not suffer and murderers, thieves, and the like would not live comfortable lives.
Perfection implies no lacking
God is also evil. The argument does not apply.
God allows evil so that the good is appreciated
God wants to be loved and is very vain. He wants to be loved so much that he allows many evils to befall mankind so that they appreciate the good more. Much as the blind man healed by Jesus appreciated his sight more because of his blindness.
God is not omniscient
Unlike the other characteristics of God, omniscience isn't necessarily required for the argument. Any situation God doesn't see can still be created as intended through the power of omnipotence.
God does Good. Satan does Evil.
God only has limited omniscience, he cannot see the future. God simply did not know that Satan would turn against him because he cannot know the future. Satan blindsided God, who lacks future knowledge, and created evil himself. God was betrayed and Satan is the reason evil exists.
If God is all-good and all-powerful, he should snuff out Satan and promptly remove all evil from the world.
Evil does not exist
As with "benevolence", "evil" can be redefined. What is "evil" for humans may not be evil for God. In fact, anything that God chooses to do can be construed as "good". Using this argument, "evil" can not exist in any definable terms when applied to God.
Besides the arguments already used in the "Tough Love" response (an all powerful God would have no reason even to appear evil) here, the apologist treads dangerously close to ethical relativism. We know from information in the bible that ethical rules have changed at the will of God. Is God, then, a relativist?
If the answer is that God is following an ethical plan, then the apologist opens himself up to the Euthyphro dilemma. If the answer is that God changes as he sees fit and anything that god declares as good is good, then what is the difference between being a relativist and following a relativist God?
When an apologist tries to redefine the premises of "the problem of evil" he finds himself in a morass of relativism, but when he tries to work with the premises he finds himself unwittingly limiting the unlimited God of his religion.
Evil is an illusion
We believe that evil exists because we view things like genocide as bad. We are simply wrong, all of these things are good.
Which suggests that everything which has ever happened is objectively good: rape, the holocaust, slavery, genocide. In order defend this theodicy, a proponent would need to agree that any horrific thing you could mention is a good thing to do.
It is all part of the plan
God's divine plan is good. What we think is evil is not, rather it's a part of God's plan we are misidentifying as evil because we cannot see the big picture.
The holocaust is part of God's divine plan? Young girls being raped and murdered is part of God's plan? If such things are part of God's plan, even without seeing the big picture one must conclude that it's a really bad plan. Furthermore, what is the point of a plan if one is all powerful? There are no steps needed; simply create the end results.
Evil is a test
Evil is needed so that God can test people.
The holocaust is a test of faith? Whose faith is tested when a child is murdered? If God is omniscient, then God already knows what humans will do in any test.
Evil is the absence of Good
Just as cold is the absence of hot and dark is the absence of light, evil is the absence of good.
This contradicts an omnipresent deity. Furthermore, if accurate then an omnipotent omnibenevolent deity should employ his omnipotence to be omnipresent in order to stand vigilant against evil.
Are evil deeds an absence of some corresponding good? Is rape an absence of unrape? Is murder an absence of unmurder? (How many people have you unraped or unmurdered today? We're committing unsins constantly!) Conversely, if baking your neighbor cookies [or name any random act of kindness] is a good deed, what is the absence of that good deed?
You bring evil on yourself
God is good and does good, but any evil you do you brought upon yourself. This is principle the theodicy of Islam.
If you are raped, you were bad. If you have a holocaust happen to you, you were bad. If something bad happens to you, you brought it on yourself. This theodicy consists of blaming the victim.
Heaven exists after this world
After you die you can go to heaven which evens everything out in the end. Regardless of what pain and suffering exists here, heaven will balance out the scales. This was often used by religious authorities to justify torture and murder during the many inquisitions and crusades. The victims' temporary agony was justified if it saved them from the eternal agony of hell.
This has nothing to do with the argument, rather it's a conclusion that it doesn't matter if there is evil, rather than address the logical consequence of a deity incompatible with an evil filled world.
One could argue that the argument above does not cover all possibilities, much like C.S. Lewis's trilemma "Liar, Lunatic or Lord", which does not consider alternate possibilities like "Legend".
However, the problem of evil can be restated as follows:
- If evil exists, and God is omniscient, then God knows about it.
- If God knows about evil, and is omnibenevolent, then he wants to prevent it.
- If God wants to prevent evil, and is omnipotent, then he can prevent it (if God wants something to happen, then it happens).
- Therefore, if God is omniscient, omnibenevolent, and omnipotent, then evil should not exist.
In this restated form, the branches of the argument follow from each other to form a reductio ad absurdum.
The problem of good
It is fairly easy to flip the argument around: if we postulate that God is all-evil, the problem of evil becomes the problem of good: why would an infinitely evil god allow good to exist?
Many or all of the arguments against the problem of evil can easily be turned around to argue against the problem of good:
- People do good deeds because God gave us free will, which in turn allows us to torment each other in ways that mere automata couldn't.
- Natural beauty, such as sunsets or the majesty of a starry sky, exists so that we may more deeply appreciate the ugliness around us.
- Mystery: while some instances of good may remain unexplained, who can claim to understand the mind of an infinitely evil god?
If the existence of evil in the universe that also includes a lot of good does not point to an infinitely evil god, then it follows that the existence of good in a universe that also includes a lot of evil does not point to the existence of an infinitely good god.
- Stanford Encyclopedia of Philosophy, The Problem of Evil
- Hume and the Evidential Problem of Evil
- Stephen Law, The God of Eth — the problem of good
- Dictionary.com entry for sophistry